# A Simple Loop Dwell Time Approach for Stability of Switched Systems

## TL;DR

This paper proposes a new simple loop dwell time method to analyze and ensure the stability of continuous-time linear switched systems with complex switching governed by graphs, including systems with unstable subsystems.

## Contribution

It introduces the simple loop dwell time concept and provides stability conditions for systems with stable and unstable subsystems, including a slow-fast switching mechanism.

## Key findings

- Derived bounds on dwell time for stability
- Ensured stability with mixed stable and unstable subsystems
- Presented a novel switching mechanism for stability

## Abstract

We introduce a novel concept of simple loop dwell time and use it to give sufficient conditions for stability of a continuous-time linear switched system where switching between subsystems is governed by an underlying graph. We present a slow-fast switching mechanism to ensure stability of the system. We also consider switched systems with both stable and unstable subsystems, and obtain bounds on the dwell time in the stable subsystem and flee time from the unstable subsystem that guarantee the stability of the system.